Recently I have read the following article: "A Continued Fraction Expansion for a Generalization of Dawson's Integral" by D. Dijkstra. I am interested on the applications given in the text. The generalization is named as F(p, x) and has uses when p=2 (Dawson's integral) and when p=3 (viscous fluid mechanics).
My question is, how is it applicated in these values of p (2 and 3) and what does the value of x mean?
Thanks in advance
The generalized Dawson integral $F(p,x)$ is defined for $p \ge 0,$ and $x\ge 0$ by $$ F(p,x) = e^{-x^p}\int_0^x e^{t^p} d t. $$ Here $p$ is a parameter and $x$ is the variable similar to the function $f(p,x) = x^p$. For $p=2$ the function $F(2,x) = D(x)$ is the ordinary Dawson function. Sample values are e.g. $$F(1,4) = 0.981684361111265820$$ $$F(3,2) = 0.092873797411695480$$ $$F(5,50)= 0.3200000008192000047\cdot10^{-7}$$